Atoms constitute relatively simple many-body systems, making them suitable objects for developing an understanding of basic aspects of many-body physics. Photoabsorption spectroscopy is a prominent method to study the electronic structure of atoms and the inherent many-body interactions. In this article, the impact of many-body effects on well-known spectroscopic features, such as Rydberg series, Fano resonances, Cooper minima, and giant resonances, is studied and related many-body phenomena in other fields are outlined. To calculate photoabsorption cross sections, the time-dependent configuration interaction singles (TDCIS) model is employed. The conceptual clearness of TDCIS in combination with the compactness of atomic systems allows for a pedagogical introduction to many-body phenomena.
REFERENCES
1.
N.
Bohr
, “On the constitution of atoms and molecules
,” Philos. Mag.
26
(151
), 1
–26
(1913
).2.
F.
Krausz
and M.
Ivanov
, “Attosecond physics
,” Rev. Mod. Phys.
81
, 163
–234
(2009
).3.
R.
Kienberger
et al., “Atomic transient recorder
,” Nature
427
(6977
), 817
–821
(2004
).4.
5.
I.
Lindgren
and J.
Morrison
, Atomic Many-Body Theory
(Springer-Verlag
, Berlin
, 1986
).6.
I.
Bloch
, J.
Dalibard
, and W.
Zwerger
, “Many-body physics with ultracold gases
,” Rev. Mod. Phys.
80
, 885
–964
(2008
).7.
P.
Fulde
, Electron Correlations in Molecules and Solids
(Springer-Verlag
, Berlin
, 2002
).8.
T.
Watanabe
, H.
Okamoto
, K.
Onomitsu
, H.
Gotoh
, T.
Sogawa
, and H.
Yamaguchi
, “Optomechanical photoabsorption spectroscopy of exciton states in GaAs
,” Appl. Phys. Lett.
101
, 082107
(2012
).9.
R.
Locht
, H.
Jochims
, and B.
Leyh
, “The vacuum {UV} photoabsorption spectroscopy of the geminal ethylene difluoride (1,1-C2H2F2). The vibrational structure and its analysis
,” Chem. Phys.
405
, 124
–136
(2012
).10.
J.
Samson
and W.
Stolte
, “Precision measurements of the total photoionization cross-sections of He, Ne, Ar, Kr, and Xe
,” J. Electron Spectrosc. Relat. Phenom.
123
, 265
–276
(2002
).11.
12.
J. B.
Foreman
, M.
Head-Gordon
, J. A.
Pople
, and M. J.
Frisch
, “Toward a Systematic Molecular Orbital Theory for Excited States
,” J. Phys. Chem.
96
, 135
–149
(1992
).13.
J. W.
Cooper
, “The Single Electron Model in Photoionization
,” in Photoionization and Other Probes of Many-Electron Interactions
, edited by F. J.
Wuilleumier
(Plenum
, New York
, 1976
), pp. 31
–47
.14.
N.
Rohringer
, A.
Gordon
, and R.
Santra
, “Configuration-interaction-based time-dependent orbital approach for ab initio treatment of electronic dynamics in a strong optical laser field
,” Phys. Rev. A
74
, 043420
(2006
).15.
L.
Greenman
, P. J.
Ho
, S.
Pabst
, E.
Kamarchik
, D. A.
Mazziotti
, and R.
Santra
, “Implementation of the time-dependent configuration-interaction singles method for atomic strong-field processes
,” Phys. Rev. A
82
, 023406
(2010
).16.
S.
Pabst
, “Atomic and molecular dynamics triggered by ultrashort light pulses on the atto- to picosecond time scale
,” Eur. Phys. J. Spec. Top.
221
, 1
–71
(2013
).17.
S.
Pabst
, L.
Greenman
, D. A.
Mazziotti
, and R.
Santra
, “Impact of multichannel and multipole effects on the Cooper minimum in the high-order-harmonic spectrum of argon
,” Phys. Rev. A
85
(023411
), 1
–8
(2012
).18.
S.
Pabst
, A.
Sytcheva
, A.
Moulet
, A.
Wirth
, E.
Goulielmakis
, and R.
Santra
, “Theory of attosecond transient-absorption spectroscopy of krypton for overlapping pump and probe pulses
,” Phys. Rev. A
86
(063411
), 1
–13
(2012
).19.
A.
Sytcheva
, S.
Pabst
, S.-K.
Son
, and R.
Santra
, “Enhanced nonlinear response of Ne8+ to intense ultrafast x rays
,” Phys. Rev. A
85
(023414
), 1
–6
(2012
).20.
M.
Marangoni
and A. M.
Sarius
, “Coupled-channel calculations of the giant dipole resonance in the one-particle-one-hole continuum approximation (I). 12C and 40Ca
,” Nucl. Phys. A
132
(3
), 649
–672
(1969
).21.
P. B.
Allen
, “Single Particle versus Collective Electronic Excitations
,” in From Quantum Mechanincs to Technology
, edited by Z.
Petru
, J.
Przystawa
, and K.
Rapcewicz
(Springer-Verlag
, Berlin
, 1996
), pp. 125
–141
.22.
R.
Santra
, “Concepts in x-ray physics
,” J. Phys. B
42
, 023001
(2009
).23.
D. P.
Craig
and T.
Thirunamachandran
, Molecular Quantum Electrodynamics
(Dover
, Mineola, NY
, 1998
).24.
A. F.
Starace
, Handbuch der Physik—Volume XXXI: Corpuscles and Radiation in Matter I
(Springer-Verlag
, Berlin
, 1982
).25.
P.
Echenique
and J. L.
Alonso
, “A mathematical and computational review of Hartree–Fock SCF methods in quantum chemistry
,” Mol. Phys.
105
(23–24
), 3057
–3098
(2007
).26.
I.
Shavitt
and R. J.
Bartlett
, Many-Body Methods in Cemistry and Physics
(Cambridge U.P.
, Cambridge
, 2009
).27.
V. L.
Sukhorukov
, I. D.
Petrov
, M.
Schäfer
, F.
Merkt
, M.-W.
Ruf
, and H.
Hotop
, “Photoionization dynamics of excited Ne, Ar, Kr and Xe atoms near threshold
,” J. Phys. B
45
(092001
), 1
–43
(2012
).28.
J.
Breidbach
and L. S.
Cederbaum
, “Migration of holes: Formalism, mechanisms, and illustrative applications
,” J. Chem. Phys.
118
, 3983
–3996
(2003
).29.
M. E.
Peskin
and D. V.
Schroeder
, An Introduction to Quantum Field Theory
(Westview Press
, New York
, 1995
).30.
Employing atomic units, the cross section is given in terms of the Bohr radius squared , which corresponds to 2.8 10–21 m2. In a more commonly used unit, this is 28 Mb.
31.
The number of photons per unit area can be calculated as the time-integrated photon flux , where is the mean photon energy of the pulse and c the speed of light in vacuo.
32.
S.
Pabst
, L.
Greenman
, and R.
Santra
, “xcid program package for multichannel ionization dynamics,” DESY, Hamburg, Germany (2012
), Rev. 681, with contributions from P. J. Ho (unpublished).33.
In order to improve the comparability of TDCIS results and experimental data, we adjusted the HF orbital energies to match the experimental binding energies from Ref. 34.
34.
A. C.
Thompson
et al., X-Ray Data Booklet
(Lawrence Berkeley National Laboratory
, Berkeley, CA
, 2001
), <
http://xdb.lbl.gov>
.35.
J. R.
Rydberg
, “La constitution des spectres d'emission des elementes chimiques
,” in Den Kungliga Svenska Vetenskapsakademiens Handlingar
(Kungliga Svenska Vetenskapsakademien
, Stockholm
, 1889)
, vol. 23
, pp. 1
–155
.36.
W. Y.
Liang
, “Excitons
,” Phys. Educ.
5
, 226
–228
(1970
).37.
The atom is simulated inside a finite numerical box, the boundaries of which conflict with the spatial extent of realistic highly excited states. By compressing these states into the box, which thereby acts as a confining potential-well, the states are shifted upwards in energy, across the ionization limit.
38.
National Institute of Standards and Technology, <http://www.nist.gov/pml/data/atomspec.cfm>.
39.
C.
Sándorfy
, The Role of Rydberg States in Spectroscopy and Photochemistry: Low and High Rydberg States (Understanding Chemical Reactivity)
(Kluwer
, Dordrecht
, 2002
).40.
M.
Glass-Maujean
, H.
Schmoranzer
, I.
Haar
, A.
Knie
, P.
Reiss
, and A.
Ehresmann
, “The J = 2 ortho levels of the v = 0 to 6 np singlet Rydberg series of molecular hydrogen revisited
,” J. Chem. Phys.
137
(084303
), 1
–10
(2012
).41.
42.
W.
Shi
and R. H.
Lipson
, “Rydberg spectra of trans-1,2-dibromoethylene
,” J. Chem. Phys.
127
, 224304
(2007
).43.
H.
Beutler
, “Über Absorptionsserien von Argon, Krypton und Xenon zu Termen zwischen den beiden Ionisierungsgrenzen2 P 3 2/0 und2 P 1 2/0
,” Z. Phys.
93
, 177
–196
(1935
).44.
U.
Fano
, “Sullo spettro di assorbimento dei gas nobili presso il limite dello spettro d'arco
,” Nuovo Cimento
N. S. 12
, 154
–161
(1935
).45.
U.
Fano
, “Effects of configuration interaction on intensities and phase shifts
,” Phys. Rev.
124
, 1866
–1878
(1961
).46.
K.
Codling
, R. P.
Madden
, and D. L.
Ederer
, “Resonances in the photo-ionization continuum of Ne I (20–150 eV)
,” Phys. Rev.
155
, 26
–37
(1967
).47.
S.
Inouye
, M. R.
Andrews
, J.
Stenger
, H.-J.
Miesner
, D. M.
Stamper-Kurn
, and W.
Ketterle
, “Observation of Feshbach resonances in a Bose-Einstein condensate
,” Nature
392
(6672
), 151
–154
(1998
).48.
T.
Kraemer
et al., “Evidence for Efimov quantum states in an ultracold gas of caesium atoms
,” Nature
440
(7082
), 315
–318
(2006
).49.
H.
Feshbach
, “Unified theory of nuclear reactions
,” Ann. Phys. (N.Y.)
5
, 357
–390
(1958
).50.
A. E.
Miroshnichenko
, S.
Flach
, and Y. S.
Kivshar
, “Fano resonances in nanoscale structures
,” Rev. Mod. Phys.
82
, 2257
–2298
(2010
).51.
F.
Reinert
and S.
Hüfner
, “Photoemission spectroscopy—from early days to recent applications
,” New J. Phys.
7
, 97
(2005
).52.
V.
Madhavan
, W.
Chen
, T.
Jamneala
, M. F.
Crommie
, and N. S.
Wingreen
, “Tunneling into a Single Magnetic Atom: Spectroscopic Evidence of the Kondo Resonance
,” Science
280
(5363
), 567
–569
(1998
).53.
B. R.
Bulka
and P.
Stefański
, “Fano and Kondo Resonance in Electronic Current through Nanodevices
,” Phys. Rev. Lett.
86
, 5128
–5131
(2001
).54.
J.
Kondo
, “Resistance Minimum in Dilute Magnetic Alloys
,” Prog. Theor. Phys.
32
(1
), 37
–49
(1964
).55.
A. S.
Sandhu
, E.
Gagnon
, R.
Santra
, V.
Sharma
, W.
Li
, P.
Ho
, P.
Ranitovic
, C. L.
Cocke
, M. M.
Murnane
, and H. C.
Kapteyn
, “Observing the Creation of Electronic Feshbach Resonances in Soft X-ray-Induced O2 Dissociation
,” Science
322
, 1081
–1085
(2008
).56.
A. E.
Miroshnichenko
, S.
Flach
, and Y. S.
Kivshar
, “Fano resonances in nanoscale structures
,” Rev. Mod. Phys.
82
, 2257
–2298
(2010
).57.
J. W.
Cooper
, “Photoionization from outer atomic subshells. A model study
,” Phys. Rev.
128
, 681
–693
(1962
).58.
U.
Fano
and J. W.
Cooper
, “Spectral distribution of atomic oscillator strengths
,” Rev. Mod. Phys.
40
, 441
–507
(1968
).59.
H. J.
Wörner
, H.
Niikura
, J. B.
Bertrand
, P. B.
Corkum
, and D. M.
Villeneuve
, “Observation of electronic structure minima in high-harmonic generation
,” Phys. Rev. Lett.
102
(103901
), 1
–4
(2009
).60.
M.
Lewenstein
, P.
Balcou
, M. Y.
Ivanov
, A.
L'Huillier
, and P. B.
Corkum
, “Theory of high-harmonic generation by low-frequency laser fields
,” Phys. Rev. A
49
, 2117
–2132
(1994
).61.
P. B.
Corkum
, “Plasma perspective on strong field multiphoton ionization
,” Phys. Rev. Lett.
71
, 1994
–1997
(1993
).62.
T. A.
Carlson
, M. O.
Krause
, F. A.
Grimm
, P.
Keller
, and J. W.
Taylor
, “Angle-resolved photoelectron spectroscopy of CCl4: The Cooper minimum in molecules
,” J. Chem. Phys.
77
, 5340
–5347
(1982
).63.
D. L.
Ederer
, “Photoionization of the 4d Electrons in Xenon
,” Phys. Rev. Lett.
13
, 760
–762
(1964
).64.
A. P.
Lukirskii
, I. A.
Brytov
, and T. M.
Zimkina
, “Photoionization absorption of He, Kr, Xe, CH4, and Methylal in the 23.6-250A region
,” Opt. Spectrosc. (USSR)
17
, 234
–237
(1964
), translated from Optika i Spektroskopiya.65.
J. W.
Cooper
, “Interaction of maxima in the absorption of Soft X Rays
,” Phys. Rev. Lett.
13
, 762
–764
(1964
).66.
M. Y.
Amusia
and J.-P.
Connerade
, “The theory of collective motion probed by light
,” Rep. Prog. Phys.
63
, 41
–70
(2000
).67.
G. C.
Baldwin
and G. S.
Klaiber
, “Photo-fission in heavy elements
,” Phys. Rev.
71
, 3
–10
(1947
).68.
E.
Khan
, “Astrophysical roles for giant resonances in exotic nuclei
,” Nucl. Phys. A
788
, 121
–129
(2007
).69.
M.
Piancastelli
, “The neverending story of shape resonances
,” J. Electron Spectrosc. and Relat. Phenom.
100
, 167
–190
(1999
).70.
C.
Kittel
, Introduction to Solid State Physics
(John Wiley & Sons, Inc.
, Hoboken, NJ, USA
, 2005
).71.
Y.
Fu
, Nonlinear Optical Properties of Nanostructures
(Pan Stanford Publishing Pvt. Ltd.
Singapore
, 2011
).72.
P.
Pattnaik
, “Surface plasmon resonance
,” Applied Biochemistry and Biotechnology
126
(2
), 79
–92
(2005
).73.
J.
Homola
, Electromagnetic Theory of Surface Plasmons
(Springer
, Berlin
, 2006
).74.
75.
B. H.
Brandsen
and C. J.
Joachain
, Physics of Atoms and Molecules
(Prentice-Hall
, Upper Saddle River, NJ
, 2003
).76.
D. C.
Mattis
, The Theory of Magnetism Made Simple
(World Scientific
, Singapore
, 2006
).77.
R.
Zitzler
, T.
Pruschke
, and R.
Bulla
, “Magnetism and phase separation in the ground state of the Hubbard model
,” Eur. Phys. J. B
27
(4
), 473
–481
(2002
).78.
79.
R.
Jordens
, N.
Strohmaier
, K.
Gunter
, H.
Moritz
, and T.
Esslinger
, “A Mott insulator of fermionic atoms in an optical lattice
,” Nature
455
(7210
), 204
–207
(2008
).80.
S.
Chandrasekhar
, “On the continuous absorption coefficient of the negative hydrogen ion
,” Astrophys. J.
102
, 223
–231
(1945
).81.
H. A.
Bethe
and E. E.
Salpeter
, Quantum Mechanics of One- and Two-Electron Atoms
(Dover, Mineola
, NY
, 2008
).82.
A. F.
Starace
, “Length and velocity formulas in approximate oscillator-strength calculations
,” Phys. Rev. A
3
, 1242
–1245
(1971
).83.
M.
Cohen
and R.
McEachran
, “Length and velocity formulae in approximate oscillator strength calculations
,” Chem. Phys. Lett.
14
(2
), 201
–204
(1972
).84.
D. L.
Lin
, “Velocity and length forms of oscillator strengths and unitary transformations of quantum electrodynamics
,” Phys. Rev. A
17
, 1939
–1943
(1978
).85.
D. H.
Kobe
, “Gauge-invariant resolution of the controversy over length versus velocity forms of the interaction with electric dipole radiation
,” Phys. Rev. A
19
, 205
–214
(1979
).86.
Ideally the integration of the cross sections should be carried out from 0 to . However, our calculations were limited to the outer subshells and therefore the upper integration boundary was fixed relative to the threshold of the most strongly bound active orbital.
87.
H.
Quiney
and F.
Larkins
, “Atomic X-ray Transition probabilities: A comparison of the dipole length, velocity and acceleration forms
,” Aust. J. Phys.
37
(1
), 45
–54
(1984
).88.
X. M.
Tong
and N.
Toshima
, “Controlling atomic structures and photoabsorption processes by an infrared laser
,” Phys. Rev. A
81
, 063403
(2010
).89.
G. C.
Schatz
and M. A.
Ratner
, Quantum Mechanics in Chemistry
(Dover
, Mineola, NY
, 2002
).© 2014 American Association of Physics Teachers.
2014
American Association of Physics Teachers
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.
